Each side of a metal plate is illuminated by light of different wavelengths. The left side is illuminated by light with λ0 = 500 nm and the right side by light of unknown λ. Two electrodes A and B provide the stopping potential for the ejected electrons. If the voltage across AB is VAB=1.2775 V, what is the unknown λ?

The  wavelength is  

Explanation:

From the question we are told that

    The  wavelength of the left light is  

      The  voltage across A  and  B is  

Let the stopping potential  at A  be and the electric potential at B  be  

The voltage across A and B is mathematically represented as

Now  According to Einstein's photoelectric equation the stopping potential at A for the ejected electron from the left side  in terms of electron volt is mathematically represented as

Where  W is the work function of the metal

             h is the Planck constant with values  

             c  is the speed of light with value

And  the stopping potential at B for the ejected electron from the right side  in terms of electron volt is mathematically represented as

So  

=>    

=>  

=>  

=>  

Where e is the charge on an electron with the value  

=>        

=>    

=>  

=>